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Lecture 2 - m 0.3048 mi ft 5280 s 3600 hr 1 hr mi 90 =...

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Lecture 2 pls-2.1 Units and Trigonometry Media: none 1. Systems of Units system distance time mass SI meter (m) second (s) kilogram (kg) cgs centimeter (cm) second (s) gram (g) English foot (ft) second (s) slug A prefix associated a unit indicates a factor of some power of 10. Examples: cm = 10 2 m, kg = 10 3 g, MJ = 10 6 J, fs = 10 15 s. 2. Units Conversion Key : multiplying (or dividing) by 1 does not change the value of an expression. Example 1: How many feet is 3.0 meters? ft 8 . 9 m 3048 . 0 ft 1 m 0 . 3 = =1
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Lecture 2 pls-2.2 Example 2: m/s 0 . 5 equals how many miles/hour? hour miles 2 . 11 hour 1 s 3600 ft 5280 mile 1 m 3048 . 0 ft 1 s m 0 . 5 = Problem solving strategy : convert all units to SI, then the answer will necessarily be in SI units. Example: SI energy unit is a 2 2 s m kg J Joule = = . If kinetic energy (KE) is given by 2 2 1 v M , what is the kinetic energy of an = M 0.3 lb baseball moving at = v 90 miles/hr? M : kg 14 . 0 lb 2.2 kg 1 lb .3 0 = v : s m 40.2 ft
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Unformatted text preview: m 0.3048 mi ft 5280 s 3600 hr 1 hr mi 90 = Therefore, its KE is ( ) ( ) J 115 40.2 0.14 2 1 2 1 2 2 = = Mv 3. Dimensional Analysis It is often useful to see if an algebraic equation is dimensionally correct, i.e., if the units are consistent. Nomenclature: [ t ] means “units of t ”. Therefore [ t ] s = if t represents time Clicker questions 1 – 3 . Lecture 2 pls-2.3 4. Trigonometry Trig functions: clicker questions 4 . Inverse trig functions: clicker question 5 Pythagorean theorem: clicker question 6 . Arc length and radians: clicker question 7 . The radian is a unitless unit because an angle expressed in radians is the ratio of two lengths, e.g., 5 m/2m = 2.5 (radians). The radian unit is used to remind you that the quantity at hand is an angle. Radians and degrees: clicker question 8 ....
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